Lec 1 - Data structures

Independent Face List

Each face stores its vertices explicitly.

struct Vertex {float x, y, z;};

struct Face {Vertex v1, v2,v3;};

struct Mesh {Face faces[F];};

Indeced Face List

Vertex array stores unique vertex coordinates only. Faces contain pointers to vertices rather than copying coordinates explicitly.

struct Vertex {float x, y, z;};

struct Face {Vretex* v1, v2, v3;};

struct Mesh { 
Vertex verts[V]; 
Face faces[F];
};

Half-edge Mesh

To efficiently store and access vertices, faces, edges and neighbors.

struct HalfEdgeMesh {
Vertex* vert; 
Halfedge* next; 
Halfedge* prev; 
Halfedge* pair; 
Face* face; 
};

struct Vertex {
float x, y, z;
Halfedge* edge; 
}; 

struct Face {
Halfedge* edge;
}; 

struct Mesh {
Vertex verts[V]; 
Face faces[F]; 
Halfedge edges[3F];
}; 

What’s an advantage with Indexed Face lists?

Memory-efficient

What’s a disadvantage with Independent Face lists?

Redundant storage

Equation for face normal assuming CCO

n_i = N_i / ||N_i||, N_i = (V_i,2 - V₁) x (V_i,3 - V₁)

Equation to normalize Normal

n_u(V₁) = n(V_i) / ||n(V_i)||

Equation for triangle area

½ ||N_i||

Equation for vertex normal

n(V₁) = sum(n_i)

Equation for area weighted vertex normal

n(V₁) = sum(A_i*n_i)